The folding of DNA in nucleosomes is accompanied by the lateral displacements of adjacent base pairs, which are usually ignored. We have found, however, that the shear deformation, called Slide, plays a much more important role in DNA folding than was previously imagined. First, the lateral Slide deformations observed at sites of local anisotropic bending of DNA define its superhelical trajectory in chromatin. (Note that the nucleosomal DNA twisting remains close, on average, to that in solution. In other words, the 'real' DNA wrapping around the histone core is inconsistent with the conventional model of superhelical DNA, which links changes in superhelical pitch to DNA twisting.) Second, the computed cost of deforming DNA on the nucleosome is sequence specific: in optimally positioned sequences the most easily deformed base-pair steps (CA:TG and TA) occur at sites of large positive Slide and negative Roll (where the DNA strongly bends, or kinks, into the minor groove). Here, we incorporate all the degrees of freedom of 'real' DNA, thereby going beyond the limits of the conventional model ignoring the lateral Slide displacements of base pairs. Note that our results are in remarkable agreement with the in vitro sequence selection (SELEX) experiments. The successful prediction of nucleosome positioning for sequences of various GC-content demonstrates the potential advantage of our structural analysis, based on calculations of the DNA deformation energy. Next, we will apply our method to the analysis of GC-rich mammalian promoters. In this regard, it is important that our knowledge-based model of nucleosome positioning takes into account the sequence-specific effects caused by linker histones (LH). LHs demonstrate a higher affinity for the AT-rich sequences at the entry-exit points of nucleosomes, which is consistent with a general tendency of AT-rich DNA for a tight compactization in chromatin. On the other hand, the GC-rich promoters are often depleted of nucleosomes and thus are easily accessible for transcription machinery. The situation is quite different, however, when DNA is methylated. In this case, the stability of nucleosomes in particular, and of chromatin in general, is increased, the promoters become less accessible, and the level of transcription is significantly decreased. The methylation-induced silencing of tumor suppressor genes is frequently related to human cancer. We link this epigenetic effect with the sequence-specific properties of LHs, known to have a higher affinity not only for the AT-rich sequences, but also for the methylated DNA. According to our model, the LHs bind to thymines and methylated cytosines through hydrophobic interactions in the major groove (submitted for publication). In addition to DNA folding in nucleosomes, the shearing deformations described above, are implicated in the sequence-specific recognition of DNA by transcription factors, such as the tumor suppressor protein p53. The DNA bending, twisting and sliding (first, predicted by us and then observed in solution upon p53 binding) are entirely consistent with the 'Kink-and-Slide' conformation described above. Therefore, structural organization of a p53 binding site in chromatin can regulate its affinity to p53 - for example, exposure of the DNA site on nucleosomal surface would facilitate the p53 binding to the response elements regulating cell cycle arrest genes (p21, GADD45, etc.). Our results indicate that there is a complex interplay between the structural codes encrypted in eukaryotic genomes - one code for DNA packaging in chromatin, and the other code for DNA recognition by regulatory proteins. Rather than being mutually exclusive (as was assumed earlier), the two codes appear to be consistent with each other. At least in some cases, such as p53 and NF--B, the DNA wrapping in nucleosomes can facilitate binding of the transcription factor to its cognate sequence, provided that the latter is properly exposed in chromatin.